Question
A cone has a radius of 12 centimeters and a height of 18 centimeters. What is the volume of the cone in cubic centimeters?
answers:
2,592 pi cm ^3
144pi cm^3
864 pi cm^3
1,296 pi cm^ 3
answers:
2,592 pi cm ^3
144pi cm^3
864 pi cm^3
1,296 pi cm^ 3
Answers
GPT-4o mini
The volume \( V \) of a cone can be calculated using the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
For the cone with a radius of \( 12 \) cm and a height of \( 18 \) cm, we can substitute these values into the formula:
\[
V = \frac{1}{3} \pi (12)^2 (18)
\]
First, calculate \( (12)^2 \):
\[
(12)^2 = 144
\]
Next, substitute \( 144 \) back into the volume formula:
\[
V = \frac{1}{3} \pi (144) (18)
\]
Now, multiply \( 144 \) by \( 18 \):
\[
144 \times 18 = 2592
\]
So the volume becomes:
\[
V = \frac{1}{3} \pi (2592)
\]
Now divide \( 2592 \) by \( 3 \):
\[
\frac{2592}{3} = 864
\]
Thus, the volume of the cone is:
\[
V = 864 \pi \text{ cm}^3
\]
Therefore, the answer is:
**864 pi cm^3**
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height.
For the cone with a radius of \( 12 \) cm and a height of \( 18 \) cm, we can substitute these values into the formula:
\[
V = \frac{1}{3} \pi (12)^2 (18)
\]
First, calculate \( (12)^2 \):
\[
(12)^2 = 144
\]
Next, substitute \( 144 \) back into the volume formula:
\[
V = \frac{1}{3} \pi (144) (18)
\]
Now, multiply \( 144 \) by \( 18 \):
\[
144 \times 18 = 2592
\]
So the volume becomes:
\[
V = \frac{1}{3} \pi (2592)
\]
Now divide \( 2592 \) by \( 3 \):
\[
\frac{2592}{3} = 864
\]
Thus, the volume of the cone is:
\[
V = 864 \pi \text{ cm}^3
\]
Therefore, the answer is:
**864 pi cm^3**